Stationary hot and cool particle distributions in the auroral magnetosphere are modelled using adiabatic assumptions of particle motion in the presence of broad-scale electrostatic potential structure. The study has identified geometrical restrictions on the type of broadscale potential structure which can be supported by a multispecies plasma having specified sources and energies. Without energization of cool thermal ionospheric electrons, a substantial parallel potential drop cannot be supported down to altitudes of 2000 km or less. Observed upward-directed field-aligned currents must be closed by return currents along field lines which support little net potential drop. In such regions the plasma density appears significantly enhanced. Model details agree well with recent broad-scale implications of satellite observations.